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anonymous
 4 years ago
find the domain of the function f(x)= 1/sqrt (4x8)
please show calculations
anonymous
 4 years ago
find the domain of the function f(x)= 1/sqrt (4x8) please show calculations

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0callum can you show the steps please

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[f(x) = \frac{1}{\sqrt{4x8}}\] now you want to look at conditions on 4x8. What can x reasonably be? Well you cannot take a square root of a negative number, and the denominator cannot be zero, so we need: \[4x8 > 0\] \[x>\frac{1}{2}\] So I was wrong above, the domain is actually: \[\left(\frac{1}{2}, \infty \right)\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0think you divided the wrong side there

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh yes sorry it's 2 lol, quite right. \[(2,\infty)\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0rickjbr can you demonstrate how you got your answer please

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0you'll have imaginary numbers if the square root is allowed to go negative

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0thus not part of the real number system

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0callum was right in his calculation 4x  8 > 0 4(x2) > 0 x2 > 0 x > 2

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yeah my reasoning was right, it's just I divided the inequality wrong and got x>1/2. rickjbr corrected this to x>2

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0thanks for the help to both of your

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0how about this. 2x^23x+5...find and simplify the difference quotient

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0The question reads Find and simplify the difference quotient f(x+h)f(x)/h for the given function f(x)=2x^(2)3x+5

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0(2(x+h)^23(x+h)+52x^2+3x5)/h

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0(2(x^2+2xh+h^2)3(x+h)+52x^2+3x5)/h

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0(2x^2+4xh+2h^23x3h+52x^2+3x5)/h

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0is that the final answer

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0checking, a bit rusty

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0my options are a)4x+2h, b)4x+2h3, c)4h+2x3, d)4h+2x, e)4x+4h

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i'll redo it, might've missed something

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0that last step was it. instead of (2h^2+4xh+3x)/h it should be (2h^2+4xh3h)/h

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0simply factor out an h

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0[h(2h+4x3)]/h =2h+4x3

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0thanks greatly. i dont know if you have the time...but im reviewing for a test and I have a whole lot of other questions. if you can't help me, i understand, i will just post on the main forum

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0probably better off posting on main forum, if i can help, i'll try

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok thanks for the help

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Find \[\frac{f(x+h)f(x)}{h}\] for \[f(x)=2x^23x+5\] \[\frac{f(x+h)f(x)}{h} = \frac{(2(x+h)^23(x+h)+5)  (2x^23x+5)}{h}\] \[= \frac{(2x^2+4xh+2h^23x3h)(2x^23x)}{h}\] \[=\frac{4xh+2h^23h}{h} = 4x+2h3\] We can verify that this is right by noting that \[f'(x) = \lim_{h\rightarrow 0}\frac{f(x+h)  f(x)}{h}\] The left hand side of this is equal to the derivative of f, which we can just do right here: \[f'(x) = 4x  3\] and we should get that this equals the limit as h goes to zero of \[\frac{f(x+h)  f(x)}{h}.\] We have already calculated that \[\frac{f(x+h)  f(x)}{h} = 4x+2h3\] so taking the limit of this as h goes to zero we get: \[\lim_{h\rightarrow 0}(4x+2h  3) = 4x+03 = 4x3.\] Hence we ave verified that the simplification has been done correctly.
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